NNLO QCD$\times$EW corrections to Z production in the $q\bar{q}$ channel

TL;DR

This paper calculates the first complete set of mixed QCD and electroweak corrections to Z boson production in quark-antiquark collisions, improving the precision of theoretical predictions for collider experiments.

Contribution

It provides the first full ${ m O}( ext{ extalpha} ext{ extalpha}_s)$ correction results, including complex two-loop integrals with elliptic functions, for Z production cross section calculations.

Findings

Complete ${ m O}( ext{ extalpha} ext{ extalpha}_s)$ corrections are now available.

Analytic evaluation of two-loop master integrals with elliptic functions.

No initial state mass singularities from weak virtual corrections at this order.

Abstract

We present the first results for the ${\cal O}(\alpha\alpha_s)$ corrections to the total partonic cross section of the process $q\bar q\to Z+X$, with the complete set of contributions, that include photonic and massive weak gauge boson effects. The results are relevant for the precise determination of the hadronic $Z$ boson production cross section. Virtual and real corrections are calculated analytically using the reduction to the master integrals and their evaluation through differential equations. Real corrections are dealt with using the reverse-unitarity method. They require the evaluation of a new set of two-loop master integrals, with up to three internal massive lines. In particular, three of them are expressed in terms of elliptic integrals. We verify the absence, at this perturbative order, of initial state mass singularities proportional to a weak massive virtual correction to the quark-gluon splitting.